Pumps & Pipes

Water Hammer Pressure — Joukowsky

Maximum pressure rise for rapid (sudden) valve closure. Wave celerity c is calculated for the pipe material; for slow closure (closure time > 2L/c) the surge will be less than this maximum.

Formula

Δ P = ρ · c · ΔV, c = √(K / (ρ · (1 + K·D / (E·t))))

Velocity change, ΔVm/s

Pipeline length, Lm

Valve closure time, tcs

Inside diameter, Dmm

Wall thickness, tmm

Pipe material (Young's modulus E)

Resultlive

Wave celerity, c: 1374.2m/s
Critical time, 2L/c: 1.4554s
Closure classed as: SLOW (use Michaud)
Joukowsky ΔP (sudden): 2061.3kPa
Joukowsky head rise: 210.12m of water
Michaud ΔP (slow closure): 750kPa
Michaud head rise: 76.453m of water

Reference: Joukowsky's equation for instantaneous closure; Michaud's linear approximation for slow closure (tc > 2L/c). Bulk modulus of water K = 2.2 GPa.